Different music skills are pretty much interelated, namely writing and reading music notation are two skills that mutually reinforce and it's hard to be very good at one, without the other. So learning to sight read "in your head", as you say, is a skill better learned as part of an overal music theory program, and usually takes a few years to acquire. But the basic building blocks are the following:
1) Learning intervals (2nd to 8ve, major, minor, perfect, ascending, descending)
2) Learning to recognize intervals by hear (begin by finding songs that have each interval and serve as a mnemonic for you, then do exercises like the one you reference to train interval identification by ear).
3) Rythmic dictation (write the heard rythm in music notation)
4) Melodic dictation (write the heard melody in music notation) of (mostly) diatonic melodies
- usually this level of study is parallel with solfege and there is mutual reinforcement between 4) and singing melodies by sight reading.
1) Learning basic diatonic chords, major and minor triads and dominant 7th
2) Learning to recognize types of diatonic chords by ear (including inversions)
3) Learning basic functional harmony
4) Learning to identify harmonic progressions by ear
5) Transcribe simple pieces by ear
- Normally the study of harmony is parallell with the study of composition, and writing your own pieces and trying them in the instrument provides an additional level of mutual reinforcement of the skills for reading and composing music.
Continue study of harmony with more complex chords and progressions
Continue to exercise transcription with progressively more complex pieces
Continue to write more complex pieces
Study instrumental and orchestral scores
The whole process may take as many as 10 years, but the basic stuff may be achieved in 1 or 2 years of applied study.